Question

How do you find the exact values of the remaining five trigonometric functions of angle, given csc of the angle is -4?

Answer 1

`csc x = 1/sin x = -4 -> sin x = -1/4`

`cos^2 x = 1 - sin^2 x = 1 - 1/16 = 15/16 -> cos x = +- sqrt15/4`

`tan x = - (1/4) (4/(sqrt15)) = (-sqr15)/15`

`cot x = -15/(sqrt15) = (-15sqrt15)/15 = -sqrt15`

`sec x = 1/cos x = -4/(sqrt15)` = `-(4sqrt15)/15`